An intimate mixture of ferric oxide and aluminium is used as solid fuel in rockets. Calculate the fuel value per `cm^(3)` of the mixture.
Heats of formation and densities are as follows:
`H_(f(AI_(2)O_(3)))^(Theta)=-399kcal mol^(-1),H_(f(Fe_(2)O_(3)))^(Theta)=-199kcal mol^(-1)`
Density of `Fe_(2)O_(3)=4.0 g cm^(-3)`, Density of `Al = 2.0 g cm^(-3)`

Explanation

`2Al+Fe_(2)O_(3) rarr Al_(2)O_(3)+2Fe, DeltaH=?`
Given, `2Al+(3)/(2)O_(2) rarr Al_(2)O_(3),DeltaH=-399.0kcal ….(2)`
`2Fe+(3)/(2)O_(2) rarr Fe_(2)O_(3),DeltaH=-199.0kcal ....(2)`
Subtracting `eq. (2)` from `eq. (1)`
`underset(Fuel mixture)(2Al+Fe_(2)O_(3))rarr 2Fe+Al_(2)O_(3), DeltaH=-200kcal`
Molecular weight of fuel mixture
`=2xx27+2xx56+48=214g`
`:' 214g` mixture produces `=200kcal `heat
`:. 1 g` mixture produces `=(200)/(214)=0.9346kcal//g`
Also volume of fusion mixture
`=vol. of Al+vol. of Fe_(2)O_(3)`
`=(54)/(2.7)+(160)/(5.2)=20+30.76=50.76mL`
`:' 50.76mL` mixture produces `=200kcal`
`:. 1 mL` mixture produces `=(200)/(50.76)`
`=3.94kcal//mL`